trait CommutativeGroup[A] extends Group[A] with CommutativeMonoid[A]
An commutative group (also known as an abelian group) is a group whose combine operation is commutative.
 Source
 CommutativeGroup.scala
 Alphabetic
 By Inheritance
 CommutativeGroup
 CommutativeMonoid
 CommutativeSemigroup
 Group
 Monoid
 Semigroup
 Serializable
 Serializable
 Any
 Hide All
 Show All
 Public
 All
Abstract Value Members

abstract
def
combine(x: A, y: A): A
Associative operation which combines two values.
Associative operation which combines two values.
Example:
scala> import cats.kernel.instances.string._ scala> import cats.kernel.instances.int._ scala> import cats.kernel.instances.option._ scala> Semigroup[String].combine("Hello ", "World!") res0: String = Hello World! scala> Semigroup[Option[Int]].combine(None, Some(1)) res1: Option[Int] = Some(1)
 Definition Classes
 Semigroup

abstract
def
empty: A
Return the identity element for this monoid.
Return the identity element for this monoid.
Example:
scala> import cats.kernel.instances.int._ scala> import cats.kernel.instances.string._ scala> Monoid[String].empty res0: String = "" scala> Monoid[Int].empty res1: Int = 0
 Definition Classes
 Monoid

abstract
def
getClass(): Class[_]
 Definition Classes
 Any

abstract
def
inverse(a: A): A
Find the inverse of
a
.Find the inverse of
a
.combine(a, inverse(a))
=combine(inverse(a), a)
=empty
.Example:
scala> import cats.kernel.instances.int._ scala> Group[Int].inverse(5) res0: Int = 5
 Definition Classes
 Group
Concrete Value Members

final
def
!=(arg0: Any): Boolean
 Definition Classes
 Any

final
def
##(): Int
 Definition Classes
 Any

final
def
==(arg0: Any): Boolean
 Definition Classes
 Any

final
def
asInstanceOf[T0]: T0
 Definition Classes
 Any

def
combineAll(as: IterableOnce[A]): A
Given a sequence of
as
, sum them using the monoid and return the total.Given a sequence of
as
, sum them using the monoid and return the total.Example:
scala> import cats.kernel.instances.string._ scala> Monoid[String].combineAll(List("One ", "Two ", "Three")) res0: String = One Two Three scala> Monoid[String].combineAll(List.empty) res1: String = ""
 Definition Classes
 Monoid

def
combineAllOption(as: IterableOnce[A]): Option[A]
Given a sequence of
as
, combine them and return the total.Given a sequence of
as
, combine them and return the total.If the sequence is empty, returns None. Otherwise, returns Some(total).
Example:
scala> import cats.kernel.instances.string._ scala> Semigroup[String].combineAllOption(List("One ", "Two ", "Three")) res0: Option[String] = Some(One Two Three) scala> Semigroup[String].combineAllOption(List.empty) res1: Option[String] = None

def
combineN(a: A, n: Int): A
Return
a
appended to itselfn
times. 
def
equals(arg0: Any): Boolean
 Definition Classes
 Any

def
hashCode(): Int
 Definition Classes
 Any

def
intercalate(middle: A): CommutativeSemigroup[A]
Between each pair of elements insert middle This name matches the term used in Foldable and Reducible and a similar Haskell function.
Between each pair of elements insert middle This name matches the term used in Foldable and Reducible and a similar Haskell function.
 Definition Classes
 CommutativeSemigroup → Semigroup

def
isEmpty(a: A)(implicit ev: Eq[A]): Boolean
Tests if
a
is the identity.Tests if
a
is the identity.Example:
scala> import cats.kernel.instances.string._ scala> Monoid[String].isEmpty("") res0: Boolean = true scala> Monoid[String].isEmpty("something") res1: Boolean = false
 Definition Classes
 Monoid

final
def
isInstanceOf[T0]: Boolean
 Definition Classes
 Any

def
remove(a: A, b: A): A
Remove the element
b
froma
.Remove the element
b
froma
.Equivalent to
combine(a, inverse(b))
Example:
scala> import cats.kernel.instances.int._ scala> Group[Int].remove(5, 2) res0: Int = 3
 Definition Classes
 Group

def
repeatedCombineN(a: A, n: Int): A
Return
a
combined with itself more than once.Return
a
combined with itself more than once. Attributes
 protected[this]
 Definition Classes
 Semigroup

def
reverse: CommutativeMonoid[A]
return a semigroup that reverses the order so combine(a, b) == reverse.combine(b, a)
return a semigroup that reverses the order so combine(a, b) == reverse.combine(b, a)
 Definition Classes
 CommutativeMonoid → CommutativeSemigroup → Monoid → Semigroup

def
toString(): String
 Definition Classes
 Any